<p>How would you solve:</p>
<p>If Sally can paint a house in 4 hours, and John can paint the same house in 6 hour, how long will it take for both of them to paint the house together?</p>
<p>Sally can paint 1/4 of a house in one hour. John can paint 1/6 of a house in one hour. So, in t hours, Sally paints (1/4)<em>t houses, and John paints (1/6)</em>t houses. Together, in t minutes they paint (1/4)<em>t+(1/6)</em>t houses. Since you need one house painted, (1/4)<em>t+(1/6)</em>t=1. t/4+t/6=1. 6t/24+4t/24=1. 6t+4t=24. 10t=24. t=2.4 hours (2 hours 24 minutes)</p>
<p>^I think that is the correct method. However, it’s been a long time since I’ve done one of these problems, so you never know.</p>
<p>((4)(6))/(4+6) = 24/10 or 2.4 hours </p>
<p>to do this you just multiply the two times together in the numerator and add them in the denominator (t1*t2)/(t1+t2)</p>
<p>^Good shortcut. OP, if you want, you can see how dkdkdk’s equation was derived based on the solution I posted.</p>
<p>LCM(4, 6) = 12
In 12 hours Sally will paint 3 houses, John - 2 houses, together - 5 houses.
12/5 = 2.4 hours per house.</p>